Biomedical Engineering Reference
In-Depth Information
The elastic modulus of bone was assigned 7300 MPa and Poisson's ratio of 0.3 (Nakamura
et al. 1981). The bone was assumed isotropic and homogeneous. Similar to the bones, the encapsu-
lated soft tissue was also modeled as a three-dimensional solid. The hyperelastic behavior of the
encapsulated soft tissue was referenced from Lemmon et al. (1997) and used a second-order energy
potential Mooney-Rivlin equation. A layer of skin was modeled on the surface of the encapsu-
lated soft tissue with a thickness of 1.2 mm (Pailler-Mattei, Bec, and Zahouani 2008) and assigned
hyperelastic material properties (Gu et al. 2010a) using an Ogden formula. Two connectors that
represented the plantar fascia were constructed with their proximal ends fixed. The distal ends were
inserted into the boundary between the proximal and distal phalanges, while a pivot point was set
at the sesamoids. The connector behavior was modeled as a slip-ring, in which material flow was
allowed at the sesamoids that could mimic the windlass mechanism. The elasticity of the connector
was assigned 203.3 MPa (Kitaoka et al. 1994).
4.2.3 l
oad
and
B
oundary
c
onditionS
An initial push-off instance was simulated with 30° metatarsophalangeal inclination (Kristen et al.
2005) that was governed by the anterior inclination of the floor plate. A vertical ground reaction
force of 30 N, which was measured by pedobarography about the corresponding phase on the nor-
mal subject, was applied under the floor plate, with the proximal end of the medial cuneiform
encrusted. The bone contact was frictionless, while the tissue-to-floor contact was assigned a coef-
ficient of friction of 0.6 (Zhang and Mak 1999).
The FE analysis simulated an initial push-off instance with passive loading that ruled out the
effects of both muscles and ligaments. The objective was to study the influence of gait loading on
the bone configurations of a normal and a hallux valgus foot. The changes of bone alignment, stress,
and loading were investigated.
4.3
ImPlICatIonS oF the FInIte element model
4.3.1 B
one
a
liGnment
and
d
iSplacement
The change of bone alignment was evaluated by the intermetatarsal angle (IMA) and the hallux
valgus angle (HVA). Axes of the bone shaft were approximated by a cylindrical regression axis
algorithm via processing software, Rapidform XOR2 (INUS Technology Ltd., Seoul, Korea), and
the axes were projected on the ground plane. The IMA was the angle between the first and second
metatarsal axes, while the HVA was the angle between the first metatarsal and phalanx axes. Figure
4.2 shows the IMAs and HVAs of the normal foot and the hallux valgus foot before the simulation
(undeformed state) and after the simulation (deformed state).
The HVA and IMA of the normal subject were 9.1° and 15.0°, respectively, while those of the
hallux valgus patient were 10.4° and 25.7°, respectively. The HVAs and IMAs of both the normal
subject and the hallux valgus patient increased after applying a forefoot loading. For the normal
subject, both the IMA and HVA increased by about 1.2 times; for the hallux valgus patient, the IMA
increased by about 140% and the HVA increased by about 89%. The increase of IMA was higher
for the hallux valgus patient compared with the normal subject, while the increase of HVA was
comparatively less. Figure 4.3 shows the simulation results indicating the displacement and change
of bone alignment after applying a forefoot loading.
4.3.2 i
influence
on
f
firSt
r
ay
J
ointS
The passive tensile force of the plantar fascia and the joint force were also evaluated. The fascia
forces of the normal foot and the hallux valgus foot were similar, with magnitudes of 25.80 N
and 24.24 N, respectively. The metatarsocuneiform joint (MC) force and metatarsophalangeal joint
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